Longitudinal equations (1-15) can be rewritten as: mu Xuu+ Xww-mg cos 0+ m(w-qUo) =Zuu+ Zww+ Zq-mg sin 000+Z Iyyg =Muu+ Mww+ Mw++ There is no roll/yaw motion, so q 0
UPTO NoW HAVE CONJSI DERED PROBLEMS RELEVANT To THE RIGID BO0Y OYNAMICS THAT ARE IMPORTANT To AEROSPACE VEHICLES USED A BODy FRAME THAT ROTATES WITH THE VEHICLE ANOTHER TMPORTANT CLASS oF PRoBLEMS FoR Bo DIES SUCH AS GyRoscofes ROToR WITH HIGH SPIN RATE ESSENTIALY MASSLESS FRAME
16.61 Aerospace Dynamics Spring 2003 Lagrange's equations Joseph-Louis lagrange 1736-1813 http://www-groups.dcs.st-and.ac.uk/-history/mathematicians/lagranGe.html Born in Italy. later lived in berlin and paris Originally studied to be a lawyer
ECTURE +2 RIGId BoDY DYNAnIC 工Ap1CAT105FA。R工 GENERAL ROTATIONAL JYNMICS EULER'S EQuATIoN of MOTIoN TORQVE fREE SPECIAL CAsEs PRIMARY LESSONS 3D RoTATONAL MOTION MUCH MORE COMPLEX
16.61 Aerospace Dynamics Spring 2003 Generalized forces revisited Derived Lagrange s equation from d'Alembert's equation ∑m(8x+16y+22)=∑(Fx+F+F。=) Define virtual displacements sx Substitute in and noting the independence of the 8q,, for each
